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1.
Jacques Laskar 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):191-196
Frequency analysis is a new method for analyzing the stability of orbits in a conservative dynamical system. It was first devised in order to study the stability of the solar system (Laskar, Icarus, 88, 1990). It is a powerful method for analyzing weakly chaotic motion in hamiltonian systems or symplectic maps. For regular motions, it yields an analytical representation of the solutions. In cases of 2 degrees of freedom system with monotonous torsion, precise numerical criterions for the destruction of KAM tori can be found. For a 4D symplectic map, plotting the frequency map in the frequency plane provides a clear representation of the global dynamics and describes the actual Arnold web of the system. 相似文献
2.
We present here the numerical application of the theoretical results derived in Correia et al. (2003, Icarus 163, 1-23) for the spin evolution of Venus since its formation. We explore a large variety of initial conditions to cover the possible formation and evolutionary scenarios. In particular, we pay special attention to the evolutions which cross the chaotic zone resulting from secular planetary perturbations (Laskar and Robutel, 1993, Nature 361, 608-612). We demonstrate that Venus’ axis can be temporarily trapped in a secular resonance with the node of Neptune’s orbit, which can prevent it from being tilted to 180° and will drive it toward 0°. We test several dissipation models and parameters to evaluate their contribution to the planet’s spin history. We confirm that despite the variations in the models, only three of the four final spin states of Venus are possible (Correia and Laskar, 2001, Nature 411, 767-770) and that the present observed retrograde spin state of Venus can be attained by two different processes. In the first scenario (π−), the axis is tilted toward 180° while its rotation rate slows down, while in the second one, the axis is driven toward 0° obliquity and the rotation rate decreases, stops, and increases again in the reverse direction to a final equilibrium value (0−). 相似文献
3.
Alexandre C. M. Correia Jacques Laskar Fran?ois Farago Gwena?l Bou�� 《Celestial Mechanics and Dynamical Astronomy》2011,111(1-2):105-130
We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20°). Using the quadrupolar non-restricted approximation for the gravitational interactions and the viscous linear model for tides, we derive the averaged equations of motion in a vectorial formalism which is suitable to model the long-term evolution of a large variety of exoplanetary systems in very eccentric and inclined orbits. In particular, it can be used to derive constraints for stellar spin-orbit misalignment, capture in Cassini states, tidal-Kozai migration, or damping of the mutual inclination. Because our model is valid for the non-restricted problem, it can be used to study systems of identical mass or for the outer restricted problem, such as the evolution of a planet around a binary of stars. Here, we apply our model to various situations in the HD 11964, HD 80606, and HD 98800 systems. 相似文献
4.
An obstacle to the asteroid mass determination lies in the difficulty in isolating the gravitational perturbation exerted by a single asteroid on the planets, being strongly correlated and mixed up with those of many other asteroids. This hindrance may be avoided by the method of analysis presented here: an asteroid mass is estimated in correspondence with its close encounters with Mars where the acceleration it induces on the planet can be sufficiently disentangled from those generated by the remaining asteroid masses to calculate. We test this technique in the analysis of range observations to Mars Global Surveyor and Mars Express performed from 1999 to 2007. For this purpose, we adopt the dynamical model of the planetary ephemeris INPOP06 (Fienga et al., 2008), which includes the gravitational influences of the 300 most perturbing asteroids of the Martian orbit. We obtain the solutions of 10 asteroid masses that have the largest effects on this orbit over the period examined: they are generally in good agreement with determinations recently published. 相似文献
5.
K. P. Sarma M. Venkateshwarlu S. K. Patil J. J. Laskar Niva Rani Devi J. Mallikharjuna Rao 《Journal of the Geological Society of India》2014,83(2):147-155
The basement gneiss of the Shillong plateau and the overlying rocks of the Shillong basin have been dissected by a number of mafic dyke swarms represented by older Proterozoic dolerite dykes and sills named as Khasi greenstone and the younger set of Cretaceous dykes. The older dolerites dykes of Shillong basin are partly metamorphosed and have undergone low-grade metamorphism compared to the fresh unmetamorphosed Cretaceous dykes dominantly exposed in the BGC of West Garo hills region. The Khasi greenstones are tholeiitic in composition and range from basalt to basaltic andesite. Most of the metamorphosed mafic dykes indicate continental nature with some amount of overlapping oceanic tectonic setting. Palaeomagnetic study of the metadolerite dykes show a direction of magnetization of Dm=29, Im=38 (α95 = 28.84; k = 48.33; N = 2) with a palaeolatitude of 21.3° N to the Indian sub-continent that clearly support the Proterozoic dyke/dyke swarm emplacement in the region. The magnetic carrier as inferred from IRM studies is magnetite in the range of psuedosingle to multi domain (MD) states with minor contribution from hematite. 相似文献
6.
We present a new set of variables for the reduction of the planetary n-body problem, associated to the angular momentum integral, which can be of any use for perturbation theory. The construction of these variables is performed in two steps. A first reduction, called partial is based only on the fixed direction of the angular momentum. The reduction can then be completed using the norm of the angular momentum. In fact, the partial reduction presents many advantages. In particular, we keep some symmetries in the equations of motion (d'Alembert relations). Moreover, in the reduced secular system, we can construct a Birkhoff normal form at any order. Finally, the topology of this problem remains the same as for the non-reduced system, contrarily to Jacobi's reduction where a singularity is present for zero inclinations. For three bodies, these reductions can be done in a very simple way in Poincaré's rectangular variables. In the general n-body case, the reduction can be performed up to a fixed degree in eccentricities and inclinations, using computer algebra expansions. As an example, we provide the truncated expressions for the change of variable in the 4-body case, obtained using the computer algebra system TRIP. 相似文献
7.
As the obliquity of Mars is strongly chaotic, it is not possible to give a solution for its evolution over more than a few million years. Using the most recent data for the rotational state of Mars, and a new numerical integration of the Solar System, we provide here a precise solution for the evolution of Mars' spin over 10 to 20 Myr. Over 250 Myr, we present a statistical study of its possible evolution, when considering the uncertainties in the present rotational state. Over much longer time span, reaching 5 Gyr, chaotic diffusion prevails, and we have performed an extensive statistical analysis of the orbital and rotational evolution of Mars, relying on Laskar's secular solution of the Solar System, based on more than 600 orbital and 200,000 obliquity solutions over 5 Gyr. The density functions of the eccentricity and obliquity are specified with simple analytical formulas. We found an averaged eccentricity of Mars over 5 Gyr of 0.0690 with standard deviation 0.0299, while the averaged value of the obliquity is 37.62° with a standard deviation of 13.82°, and a maximal value of 82.035°. We find that the probability for Mars' obliquity to have reached more than 60° in the past 1 Gyr is 63.0%, and 89.3% in 3 Gyr. Over 4 Gyr, the position of Mars' axis is given by a uniform distribution on a spherical cap limited by the obliquity 58.62°, with the addition of a random noise allowing a slow diffusion beyond this limit. We can also define a standard model of Mars' insolation parameters over 4 Gyr with the most probable values 0.068 for the eccentricity and 41.80° for the obliquity. 相似文献
8.
Jacques Laskar 《Celestial Mechanics and Dynamical Astronomy》1996,64(1-2):115-162
Large scale chaos is present everywhere in the solar system. It plays a major role in the sculpting of the asteroid belt and in the diffusion of comets from the outer region of the solar system. All the inner planets probably experienced large scale chaotic behavior for their obliquities during their history. The Earth obliquity is presently stable only because of the presence of the Moon, and the tilt of Mars undergoes large chaotic variations from 0° to about 60°. On billion years time scale, the orbits of the planets themselves present strong chaotic variations which can lead to the escape of Mercury or collision with Venus in less than 3.5 Gyr. The organization of the planets in the solar system thus seems to be strongly related to this chaotic evolution, reaching at all time a state of marginal stability, that is practical stability on a time-scale comparable to its age.This lecture was given at the XIth International Congress of Mathematical Physics, Paris, july 1994 相似文献
9.
Monopod caisson foundation is a viable alternative for supporting offshore wind turbines located at shallow water depths. This foundation system has to resist overturning moment generated due to resultant lateral load, arising from wind and water wave action, that can act at any loading height above the seabed. This paper presents results of a numerical investigation performed to determine the influence of loading height, caisson geometry and superstructure load on the ultimate lateral capacity, initial stiffness, and soil failure zone of the foundation, when installed in very dense sand. Both the ultimate and serviceable states of the caisson foundation obtained from the analyses are represented in terms of envelopes plotted between lateral load and overturning moment. Simplified expressions, which take into account the influence of caisson geometry, loading height, and soil properties, are also presented to serve as a preliminary base for design of the monopod caisson foundation. 相似文献
10.
Evaluation of Composts from Agricultural Wastes with Fish Pond Sediment as Bulking Agent to Improve Compost Quality 总被引：1，自引：0，他引：1
Tanmoy Karak Pradip Bhattacharyya Ranjit Kumar Paul Tapati Das Subhrajit K. Saha 《洁净——土壤、空气、水》2013,41(7):711-723
Composts with five different ratios of agricultural wastes, viz. rice straw (RS), wheat straw (WS), potato plant (PP), and mustard stover (MS) were prepared with or without fish pond bottom sediment to investigate the compost maturity and their suitability for field application. The composting process was monitored through the changes in physico‐chemical parameters and germination index (GI) at every 7 days interval of the composting process. All the composts were dark brown and smelled like forest soil within 56 days of composting, which reflected its matured status. On the basis of the physico‐chemical parameters (bulk density: 0.84 g/cm3; pH 7.05; electrical conductivity: 3.52 mS/cm; cation exchange capacity:82.4 cmol/kg; total carbon:321.4 g/kg; total nitrogen: 16.9 g/kg; As: 6.8 mg/kg; Cd: 2.96 mg/kg; Cr: 29.6 mg/kg, Cu: 243.6 mg/kg; Hg: 0.019 mg/kg; Ni: 24.3 mg/kg; Pb: 62.1 mg/kg and Zn: 812 mg/kg) and GI (89–96%), it could be concluded that RS/WS/PP/MS, 1:1:2:1 v/v/v/v with fish pond sediment produced better compost in accordance with the Indian compost standard. Application of a combined randomized block design analysis revealed that there is a significant difference in the responses of the five composts, in relation to the time of composting. Hierarchical clustering algorithm was applied with a view to form homogeneous groups of five different composts on the basis of different physico‐chemical parameters. Therefore, the ratio of waste incorporation is an important decision for composting and addition of pond sediment can improve the quality of compost. 相似文献